278080 Development and Application of a Heuristic to Study Heterogeneous Nucleation Mechanisms

Monday, October 29, 2012: 1:30 PM
415 (Convention Center )
Geoffrey P. F. Wood1, Keith Chadwick1, Erik E. Santiso2 and Bernhardt L. Trout1, (1)Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA, (2)Imperial College London, London, United Kingdom

The key tool for understanding the properties of discrete atomic and molecular clusters is identifying their energetic global minimum configuration. However, even for simple pair potential models the search for the global minimum has been shown to be a member of the so-called "NP-hard" class of problems.[1] Additional studies[2][3][4] have estimated that the growth in the number of local minima is of the order ~exp(N), where N is the number of components. Moreover, the sequence of global minima as a function of the size of the cluster typically forms a set whose members vary dramatically in morphology. This gives rise to the frequent occurrence of magic numbers in cluster growth experiments. These observations demonstrate that in order to solve this optimization problem efficiently, unbiased heuristic methods are needed. The algorithms that have shown the most promise include: simulated annealing,[5] Monte Carlo basin hopping[6] and genetic (or evolutionary) algorithms (GA or EA).[7] Each class of algorithm has been successful at locating the global minima in a variety of different chemical contexts using a diverse range of potential energy functions. However, in some cases they still scale poorly with system size. In addition, because of their stochastic nature they do not guarantee that the global minimum will be found for any particular simulation. To address the issues of scalability and efficiency in global optimizations of atomic and molecular clusters we develop and carefully assess a heuristic that combines the genetic algorithm with quenched molecular dynamics simulations against a series of benchmark systems.  We then summarize the results of using the algorithm to find the species responsible for initiating a novel cooperative heterogeneous nucleation mechanism.

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[7]        (a) De Jong, K. A. An Analysis of the Behavior of a class of Genetic Adaptive Systems. Ph.D. thesis, University of Michigan, Ann Arbour, MI, 1975. (b) Holland, J. H.; Adaptation in natural and artificial systems: an introductory analysis with applications to biology, control, and artificial intelligence; MIT press: Cambridge, 1992. (c) Goldberg, D. E.; Genetic algorithms in search, optimization, and machine learning; Addison-Wesley Longman Pub. Co.: Boston, 1989.

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